Diffraction grating equation for maxima

Steps:

• Slit spacing d = 1 / (450 lines/mm × 10^3 mm/m) = 2.22 × 10^{-6} m.
• Wavelength λ = 680 nm = 6.80 × 10^{-7} m.
• For second order (m=2), sinθ = mλ / d = (2 × 6.80 × 10^{-7}) / 2.22 × 10^{-6} = 0.612.
• θ = sin^{-1}(0.612) = 38°.

Why D is correct:

• The grating equation d sinθ = mλ directly gives θ = 38° for m=2, matching the second-order maximum.

Why the others are wrong:

• A. 1.8° is far too small, possibly from dividing wavelength by lines incorrectly.
• B. 3.5° underestimates the angle, likely from using mm instead of m for d.
• C. 18° is the first-order maximum (m=1), not second-order.

Final answer: D